{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import  pickle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append(\"./src\")\n",
    "from evals import *\n",
    "from optimization import *\n",
    "from gauss_update import *\n",
    "from gaussian_process import *\n",
    "from kinetic_model import *\n",
    "from mpc import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load waypoints"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f9e9f7a3438>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "with open('waypoints.binaryfile', 'rb') as td:\n",
    "    waypoints = pickle.load(td)\n",
    "    \n",
    "cx,cy = waypoints[:,0],waypoints[:,1]\n",
    "plt.scatter(cx,cy,color='red',s=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load training data (59 records collected using inaccurate dynamics model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import  pickle\n",
    "with open('training_data.binaryfile', 'rb') as td:\n",
    "    data = pickle.load(td)\n",
    "pos = torch.cat([d[0].view(1,-1) for d in data ] , dim=0)\n",
    "label = torch.cat([d[1].view(1,-1) for d in data ] , dim=0)\n",
    "pred = torch.cat([d[2].view(1,-1) for d in data ] , dim=0)\n",
    "cont_dt = torch.cat([d[3].view(1,-1) for d in data ] , dim=0)\n",
    "x = torch.cat([pos[:,2:],cont_dt[:,:-1]],dim=1)\n",
    "label_ = label[:,2:4]\n",
    "pred_ = pred[:,2:4]\n",
    "y = (label_ - pred_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### train Gaussian-Process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "gp_model = GaussianProcess(dim_x=6,dim_y=2,var=0.01)\n",
    "gp_model.train(x,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### define process-model(inaccurate) and acutual-car-model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# inaccurate process_model\n",
    "p_model = vehicle_model(WB=2.5) \n",
    "\n",
    "# actual_car_model\n",
    "real_car_model = vehicle_model(WB=1.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Run MPC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "len_horizon = 10\n",
    "TMAX = 200\n",
    "step = 0\n",
    "sigma_w = 0.01\n",
    "start = 1\n",
    "speed = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-9-292cf16b2503>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     31\u001b[0m     \u001b[0mmpc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mGP_MPC\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgp_propagator\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mconstruct_loss_\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlen_horizon\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mwaypoints\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     32\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 33\u001b[0;31m     \u001b[0mcontrols_dt\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mpath\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mvars_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmpc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstate0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0m_controls\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mvs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mdt\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mstart\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0m_vars\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     34\u001b[0m     \u001b[0mcontrols\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcontrols_dt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     35\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/pyworks/gaussian_mpc/src/mpc.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, state_init, controls_init, vs, dt, start, _vars)\u001b[0m\n\u001b[1;32m     47\u001b[0m             \u001b[0mopt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzero_grad\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     48\u001b[0m             \u001b[0mloss\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mevaluate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpath\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mrefs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mvs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0m_vars\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 49\u001b[0;31m             \u001b[0mloss\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbackward\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mretain_graph\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     50\u001b[0m             \u001b[0mopt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstep\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     51\u001b[0m             \u001b[0mopt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzero_grad\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.local/lib/python3.6/site-packages/torch/tensor.py\u001b[0m in \u001b[0;36mbackward\u001b[0;34m(self, gradient, retain_graph, create_graph)\u001b[0m\n\u001b[1;32m    105\u001b[0m                 \u001b[0mproducts\u001b[0m\u001b[0;34m.\u001b[0m \u001b[0mDefaults\u001b[0m \u001b[0mto\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m`\u001b[0m\u001b[0;31m`\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;31m`\u001b[0m\u001b[0;31m`\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    106\u001b[0m         \"\"\"\n\u001b[0;32m--> 107\u001b[0;31m         \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mautograd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbackward\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgradient\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mretain_graph\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcreate_graph\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    108\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    109\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mregister_hook\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhook\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.local/lib/python3.6/site-packages/torch/autograd/__init__.py\u001b[0m in \u001b[0;36mbackward\u001b[0;34m(tensors, grad_tensors, retain_graph, create_graph, grad_variables)\u001b[0m\n\u001b[1;32m     91\u001b[0m     Variable._execution_engine.run_backward(\n\u001b[1;32m     92\u001b[0m         \u001b[0mtensors\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgrad_tensors\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mretain_graph\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcreate_graph\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 93\u001b[0;31m         allow_unreachable=True)  # allow_unreachable flag\n\u001b[0m\u001b[1;32m     94\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     95\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "# define gp_propagator (used to compute sequence of uncertainties of control accuracy)\n",
    "gp_propagator = gaussian_propagator(p_model.forward,gp_model.forward,sigma_w)\n",
    "\n",
    "# define initial state\n",
    "x0,y0,gx0,gy0 = waypoints[start]\n",
    "v0 = torch.sqrt(gx0.pow(2)+gy0.pow(2))*speed\n",
    "yaw0 = torch.atan2(gy0,gx0)\n",
    "delta0=torch.zeros(1)\n",
    "a0=torch.zeros(1)\n",
    "state0 = torch.cat( [x0.view(1),y0.view(1),yaw0.view(1),v0.view(1),delta0,a0])\n",
    "\n",
    "# initialize estimate of uncertainty of control accuracy\n",
    "vars0 = torch.ones(len_horizon)*0.1\n",
    "_vars=vars0\n",
    "\n",
    "# define first control input (not changing speed and steering angle) to be optimized later\n",
    "_controls = torch.nn.Parameter(torch.zeros(len_horizon,2))\n",
    "\n",
    "# define speed (constant velocity) \n",
    "dt = torch.ones(len_horizon,1)\n",
    "vs = torch.LongTensor(torch.arange(len_horizon+1))*speed\n",
    "\n",
    "real_path = []\n",
    "\n",
    "for T in range(TMAX):\n",
    "    if T>0:\n",
    "        start = start_\n",
    "        _controls = controls_.data.clone()\n",
    "        \n",
    "    # make prediction with MPC (inaccurate_model + gaussian_process)\n",
    "    mpc = GP_MPC(gp_propagator,construct_loss_,len_horizon,waypoints)\n",
    "\n",
    "    controls_dt,path,vars_ = mpc.run(state0,_controls,vs,dt,start,_vars)\n",
    "    controls = controls_dt[:,:-1]\n",
    "    \n",
    "    # measure actual state \n",
    "    state_real = real_car_model.forward(state0,controls_dt[0])\n",
    "    real_path.append(state_real.view(1,-1))\n",
    "\n",
    "    controls_ = _controls.data.clone()\n",
    "    controls_[:-(step+1)] = _controls[step+1:]\n",
    "    controls_[-(step+1):]=0\n",
    "    start_ = search_(state_real,waypoints,start,L=(speed+1)*len_horizon)\n",
    "    \n",
    "    state0 = state_real.data.clone()\n",
    "    _vars = vars_.data.clone()\n",
    "    \n",
    "    # visualization\n",
    "    _x = torch.cat(real_path,dim=0)[:,0].data.numpy()\n",
    "    _y = torch.cat(real_path,dim=0)[:,1].data.numpy()\n",
    "    \n",
    "    x_ = path[:,0].data.numpy()\n",
    "    y_ = path[:,1].data.numpy()\n",
    "    \n",
    "    plt.scatter(_x,_y,color='blue',s=30)\n",
    "    plt.scatter(x_,y_,color='green',s=20)\n",
    "    plt.scatter(cx,cy,color='red',s=1)\n",
    "    im = plt.draw()\n",
    "    s_zero = str(T).zfill(4)\n",
    "    '''\n",
    "    fn = \"./figs/fig\"+str(s_zero)+\".png\"\n",
    "    plt.savefig(fn)\n",
    "    '''\n",
    "    plt.pause(0.01)"
   ]
  }
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